GCF of 975/208, 415/305, 870/220
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 975/208, 415/305, 870/220 i.e 5/697840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/208, 415/305, 870/220.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 975/208,415/305,870/220?
Given fractions are 975/208,415/305,870/220
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 975/208,415/305,870/220, numerators are 975,415,870
Denominators are 208,305,220
The GCF of 975,415,870 is 5 .
LCM of 208,305,220 is 697840.
The greatest common factor of 975/208,415/305,870/220 = [GCF of 975,415,870]/[LCM of 208,305,220]= 5/697840
Therefore, the GCF of 975/208,415/305,870/220 is 5/697840.
To find the highest common factor of 975,415,870, we have to find the factors of both numbers and list the highest common factor.
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The factors of 415 are 1, 5, 83, 415
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 975,415,870 is 5.
Lets's calculate GCF of 975,415,870
| 5 | 975, 415, 870 |
| 195, 83, 174 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 975,415,870 By Matching Biggest Common Factor Method
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 975,415,870 . The biggest common factor number is the GCF number.
So the greatest common factor 975,415,870 is 5.
Lets's calculate LCM of 208,305,220
| 2 | 208, 305, 220 |
| 2 | 104, 305, 110 |
| 5 | 52, 305, 55 |
| 52, 61, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 52 x 61 x 11 = 697840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/697840
Therefore, the GCF of Fractions 975/208,415/305,870/220 is 5/697840
Least Common Multiple of 208,305,220 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 208,305,220 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,305,220) = 1
common factors(in case of two or more numbers have common factors) = 20
GCF(208,305,220) x common factors =1 x 20 = 20
LCM(208,305,220) = ( 208 × 305 × 220 ) / 20
LCM(208,305,220) = 13956800 / 20
LCM(208,305,220) = 697840
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FAQs on GCF of Fractions of 975/208, 415/305, 870/220
1. What is the HCF of 975,415,870?
The HCF of 975,415,870 is 5
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 975/208, 415/305, 870/220?
Answer: GCF of Numerators as per given numbers 975/208, 415/305, 870/220 is
GCF of Numerators i.e. for 975,415,870 is 5
LCM of denominators i.e. for 208,305,220 is 697840.
Thus, GCF of Fractions is 5/697840.Finally, GCF of Fractions for 975/208, 415/305, 870/220 is 5/697840.